Oh, that sounds a bit hard to do
So you're saying that you want to render the mod_list_article, but only display it if it has some articles to display? and the same for mod_related_anything?

MetaMod doesn't actually give you the ability to render modules in advance and examine their contents. So on the face of it, it doesn't look hopeful.

However, can I ask what mod_list_article actually does? Does it just list articles in a specific category? Or some other criteria like that? If so, then the MetaMod could basically do the same lookup that mod_list_article does, then decide to show/hide the mod_list_article module based on that.

I suppose theoretically we could do the same thing for mod_related_anything, but it might be a bit harder to get at the same SQL query that it's doing, in order to replicate it.

If you can dig around and find the exact SQL that's being run for each of these modules, then post it here and I'll show you how to use that info in MetaMod.

Cheers,
Stephen